It always seemed likely this was going to be one of those Stuart Broad days from the moment, five overs into New Zealand's invertebrate second innings, that Hamish Rutherford's off stump was uprooted and sent spinning back in the direction of the pavilion like a dying catherine wheel. It was a lovely sight — you don't see the cartwheel so often these days — and a lovely ball from Broad delivered on that brilliantly challenging full length that his height makes so difficult to judge, the ball running across the left-hander just enough to elude the defensive prod.

From there on in, an hour before lunch and an hour afterwards, there was bounteous evidence of the qualities that can alter the direction of a Test match but which have also frustrated England's management at times. When Broad is good he's very, very good. When he's bad – or rather oddly lacking in spark – he's doing pretty much what he does the rest of the time.

Perhaps it might seem mean-spirited to linger on Broad's unusually disparate highs and lows on the day he produced his Test-best figures of seven for 44 and looked in the process like an irresistible force of galloping, straight-lined athleticism. But then this does seem to be his lot: a bowler who at his best looks so devastatingly incisive but whose destiny it is to be discussed mainly in terms of why those times do not come more often.

Broad set New Zealand's collapse in motion, inducing a horribly stiff-looking fence from Peter Fulton at a ball that left him a little. The Kiwis had been set a daunting but far from unassailable 239 to reel in what would have been just their ninth Test victory against England in 98 attempts. In the event Broad simply skated through their top order.

Two balls after Rutherford's dismissal Ross Taylor was caught at slip from a delivery on that same horribly in-between length, shaping away just enough to induce a hard-handed prod. At that stage Broad had three for nine in 13 balls and there was that familiar sense in the air of unbound possibilities as he ran in from the Nursery End, a vision of effortless menace. His first five wickets came in 5.3 overs as a finely-poised Test match was effectively decided in 40 minutes.

Broad would later suggest he was helped by the wicket quickening up. It is hard to tell if this is simply modesty (which in fairness, it probably is: he is a great team man) or a pre-empting of the inevitable question as to why Broad o'clock, from The Oval, to Trent Bridge and now back to Lord's again, does not strike rather more often.

"It's about rhythm," he said afterwards. "As a bowler I felt my stride pattern was pretty good. I just hit my straps OK. I felt in a nice rhythm and it happens like that – some days you get the nicks some days you don't."

In a wider sense this is what England have come to expect, a level of part-time brilliance that has to date added up to a fine if patchily constructed set of Test statistics. Broad has been playing Test cricket for six years. If his record that time has steadily improved, his progress is still based around a series of staccato peaks. In the last two years Broad has taken 91 wickets at just over 26 and has four five-fors in the past year. And yet there have been seven Tests in that period where he has taken two or fewer wickets and 19 such in his career.

It is to be expected that bowlers should thrive in certain conditions: perhaps with Broad the frustration stems from the fact that often it seems to be something in him rather than pitch, skies or ball — some jiggling of his internal motors, the location of that perfect length — that sparks his better days.

When it swings, as it did here, his ability to drift the ball in and out at consistently high pace creates an irresistible mini weather-front of pressure. New Zealand fell to pieces in the face of wonderfully tight bowling at both ends, the shambolic run out that sealed England's victory symptom of a batting order in a state of suffocation. In that period Broad scarcely bowled a short ball, instead generating a tangible sense of menace from that devilish length and the force of his own hustling presence. And never mind the off-days for now. Proof of those enduring match-turning qualities — not to mention some talk that the ball that got Rutherford is a new-found speciality against left-handers — all augurs well for sterner tests later this summer.